### Introduction

The core technique available to Project Managers for planning and controlling their projects is Network Analysis. This short guide will provide a basic understanding of networking principles before applying them.

Network Analysis, Critical Path Analysis (CPA), or the American “Program, Evaluation, and Review Technique” (PERT) is one of the classic methods of planning and controlling the progress of projects.

### Tasks or Activities

Effective planning of projects requires careful thought and the application of logic. To illustrate this planning tool, let’s consider the manufacturing process of a small item. Some typical processes might be:

*cutting**finishing**assembling**purchasing**machining**testing**designing*

All these processes are called ‘ACTIVITIES’ or ‘TASKS.’

### Step 1:

List WHAT has to be done.

Hint: try thinking of verbs ending in “…ing”, like machining or testing.

Do not consider, at this stage, who is going to do what, concentrate on the WHAT only.

An activity or task is represented by a rectangle, thus:

### Step 2:

Decide the ORDER in which the tasks must be done.

Some steps are obvious. We, perhaps, cannot test until assembly has been completed, which cannot be done until the various parts have been made. So, we have a logical relationship between the start of one task and the beginning of the next. We could order our list of tasks as shown:

*designing purchasing cutting machining assembling testing finishing*

### Logic Network or PERT Chart

Writing this out as a network looks like this:

We put the tasks into rectangles and join them with arrows to show the sequence or precedence or the logical relationships between them.

Suppose that once we have bought the materials, some need cutting to size and others need turning on a lathe. The tasks of machining and cutting could run in parallel rather than consecutively, assuming we have the appropriate resources. But, let’s add a bit more to our process. Say the cut parts need to be welded together before assembling — like this:

Let’s add another task: the writing of a set of test instructions. Where would writing fit in? Well, the writing cannot really start until the design is finished, though it could be carried out at the same time as the fabrication. It must be ready before the testing can begin. Applying such logic to the relationships, we can add the task writing like this:

Now let’s say we need to have our draughtsman produce some illustrations for our test instructions. When the writing and the drawing are finished, we will then need to edit the whole as shown:

And, so the network is built up, often cuing the mind to missing tasks.

In this step, always assume you have infinite resources so that who does what does not cloud the issue – concentrate only on the LOGIC.

### Time Analysis

### Duration

Having completed the network, we can begin the analysis. Firstly, we need to know the duration of each task and write it into the network. For convenience, we will write the durations in days, as shown:

In this step, always reduce the resource requirement to the duration of ONE person to give maximum flexibility to add further resources later when the project begins to run late. There are rare cases when tasks cannot physically be performed by one resource. In which case, consider the time taken for both of them working together. For example, for carrying a very long plank that requires a person at each end, adding more resources will not necessarily reduce the duration. In fact, it might even slow it down if they get in the way of each other, but you must have two. Checking the brake lights on a car is another example.

### The Forward Pass

Now we can calculate how long the project will take. We start by calculating the shortest time or ‘earliest finish.’ If we start at time ‘0,’ the earliest day that design can be finished is day 10. Purchasing; therefore, cannot start until day 10 (i.e. the earliest we can start purchasing is day 10), and thus the earliest finish for purchasing is 10 + 21 = day 31. We write the earliest start time in the top left-hand corner of the task box, and the earliest finish time over the right-hand corner of the task box.

For the purchasing task, we say the Earliest Start Time (EST) is 10 and the Earliest Finish Time (EFT) is 31.

The earliest time both cutting and machining can start is day 31. So, the earliest finish for cutting will be day 36, and for machining, day 39. However, assembly cannot start at day 39 because the welding has not yet been done. The earliest welding can start is after the cutting is finished (i.e. day 36). The earliest time assembly can start must be day 42.

Note that the task machine has some float or slack (i.e. it cannot start before day 31 and must finish before day 42, but as it only takes 8 days, there is a slack of 42 – 31 – 8 = 3 days. When calculating the earliest times, you must consider all the paths or arrows coming into the task box, and select the largest or longest time. Now if we complete the timings, or “Forward Pass” as it is called, the picture will look like this:

The calculations show that the whole project will take 52 days, or that the ‘earliest finish time’ is 52 days.

### Slack

You will remember that when we considered the task machine we found that it had some slack available. You will have noted that the tasks along the paths draw, write, and edit also had some slack. The other tasks (i.e. those with no slack) are critical in that any delay in their completion will cause the whole project to be late. It is thus very important to discover the critical tasks and identify the critical path through the network.

### Critical Path

The next part of the analysis of the network is to find the CRITICAL PATH. By definition the Critical Path is the shortest time path through the network. In such a simple network, it is easy to calculate the amount of slack available for each task, but in a complicated network, it is not easy to ‘see’ which tasks have slack and which have none.

### The Backward Pass

So far we have calculated the Earliest Start Time (EST) and the Earliest Finish Time (EFT) for each task. The next step in calculating the critical path is to re-time the network starting at the end and calculate the Latest Start Time (LST) and Latest Finish Time (LFT) for each task.

So, beginning with the earliest finish time for the whole project (i.e. 52 days), we subtract the time of the last task giving 49 days as the latest time the finishing task can begin without affecting the outcome.

The latest time we can start testing is 49 – 2 = 47 days, and assembly in 42 days. Continuing backwards, against the arrows (doing what is called the “backward pass”), the latest time welding can start is 42 – 6 = 36 days.

But, what about cutting and machining? What is the latest time purchasing can finish? Well, the latest time machining could start is 42 – 8 = day 34, and the latest time cutting could start is 36 – 5 = day 31. Hence, the latest time purchasing can finish is day 31.

So when making the backward pass to calculate the latest times, you have to consider all the arrows coming out of a task box and select the lowest or shortest time to that task.

Now to finish the backward pass we calculate the latest times for design to finish and start. The latest time writing could start is 42 – 14 = day 28, the latest time drawing can start is 42 – 8 = 34, and the latest time purchasing can start is 31 – 21 = day 10. Therefore, the latest time design can finish without affecting the project finish time is day 10. Subtracting the time of the design task leaves us at day 0, which is back to our starting point!

### Slack, Again

Now that we have completed the timings by a forward and backward pass, we can look for slack. In this simple network, it is easy to see that the tasks machine, draw, and write have slack. As we have already discovered, machining can start at day 31 but must finish by day 42. As it takes only 8 days to complete, the slack is 3 days. We will write the slack in the empty slot in the bottom center of the box. With writing, the task must finish by day 42, but it can start at day 10. As it takes 14 days to complete, writing has a slack of 24 – 42 = 18 days. Similarly, drawing has a slack of 24 days and editing 18 days. The remaining tasks have no slack at all.

### The Critical Path

So, to find the critical path, we look first at the tasks who’s earliest and latest start times are identical. Then, we determine which path between such tasks has no slack. That path is, then by definition, the critical path. On the diagram below, the critical path is indicated by bold lines.

Well, there we are!

The critical path has been identified, we know the total time of the project, and we know how much slack there is in the non-critical tasks. We have a structured a plan that is logical and ordered. All we have to do now is assign resources, put it into action, and control the results!

## 2 Comments

Crystal clear explanation, Mike.

So much of the difficulty that I see people having with MS Project can be traced to an inadequate understanding of the critical path method.

Of course it is essential that anyone using MS Project should understand the critical path method, and by “understand” I mean actually do the calculations in order to experience how the algorithm works. But it is really only necessary to do the calculation once, and after that the software does it.

Thanks Trevor. That is precisely why I wrote the guide in the first place! I first produced it as a self-training guide where the student had to work through the project, answering a question on one page, getting the answer and a new question on the next page, gradually building up the project step by step. It seemed to work well!

Mike

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